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C:/php5/PEAR/Math/Numerical/RootFinding/_[ Writable ]

File:C:/php5/PEAR/Math/Numerical/RootFinding/NewtonRaphson2.php

<?php
/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4 foldmethod=marker: */

// {{{ Header

/**
 * Driver file contains Math_Numerical_RootFinding_Bisection class to provide
 * Newton-Raphson 2 method root finding calculation.
 *
 * PHP versions 4 and 5
 *
 * LICENSE:
 *
 * BSD License
 *
 * Copyright (c) 2004-2006 Firman Wandayandi
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above
 *    copyright notice, this list of conditions and the following
 *    disclaimer in the documentation and/or other materials provided
 *    with the distribution.
 * 3. Neither the name of Firman Wandayandi nor the names of
 *    contributors may be used to endorse or promote products derived
 *    from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 * @category Math
 * @package Math_Numerical_RootFinding
 * @subpackage Methods
 * @author Firman Wandayandi <firman@php.net>
 * @copyright Copyright (c) 2004-2006 Firman Wandayandi
 * @license http://www.opensource.org/licenses/bsd-license.php
 *          BSD License
 * @version CVS: $Id: NewtonRaphson2.php,v 1.1 2006/01/30 18:42:00 firman Exp $
 */

// }}}
// {{{ Dependencies

/**
 * Load Math_Numerical_RootFinding_Common as base class.
 */
require_once 'Math/Numerical/RootFinding/Common.php';

// }}}
// {{{ Class: Math_Numerical_RootFinding_NewtonRaphson2

/**
 * Newton-Raphson 2 method class.
 *
 * @category Math
 * @package Math_Numerical_RootFinding
 * @subpackage Methods
 * @author Firman Wandayandi <firman@php.net>
 * @copyright Copyright (c) 2004-2006 Firman Wandayandi
 * @license http://www.opensource.org/licenses/bsd-license.php
 *          BSD License
 * @version Release: 1.0.0
 */
class Math_Numerical_RootFinding_NewtonRaphson2
extends Math_Numerical_RootFinding_Common
{
    // {{{ Constructor

    /**
     * Constructor.
     *
     * @param array $options (optional) Options.
     *
     * @access public
     * @see Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common()
     */
    function Math_Numerical_RootFinding_NewtonRaphson2($options = null)
    {
        parent::Math_Numerical_RootFinding_Common($options);
    }

    // }}}
    // {{{ infoCompute()

    /**
     * Print out parameters description for compute() function.
     *
     * @access public
     */
    function infoCompute()
    {
        print "<h2>False Position::compute()</h2>\n" .

              "<em>float</em> | <em>PEAR_Error</em> " .
              "<strong>compute</strong>(<u>\$fxFunction</u>, " .
              "<u>\$dfx1Function</u>, <u>\$dfx2Function</u>, " .
              "<u>\$xR</u>)<br />\n" .

              "<h3>Description</h3>\n" .
              "<em>callback</em> <u>\$fxFunction</u> Callback f(x) equation " .
              "function or object/method tuple.<br>\n" .

              "<em>callback</em> <u>\$dfx1Function</u> Callback f'(x) " .
              "equation function or object/method tuple.<br>\n" .

              "<em>callback</em> <u>\$dfx2Function</u> Callback f''(x) " .
              "equation function or object/method tuple.<br>\n" .

              "<em>float</em> <u>\$xR</u> Initial guess.<br>\n";
    }

    // }}}
    // {{{ compute()

    /**
     * Newton-Raphson method for calculate double root (twin root).
     *
     * @param callback $fxFunction Callback f(x) equation function or
     *                             object/method tuple.
     * @param callback $dfx1Function Callback f'(x) equation function or
     *                              object/method tuple.
     * @param callback $dfx2Function Callback f''(x) equation function or
     *                              object/method tuple.
     * @param float $xR Initial guess.
     *
     * @return float|PEAR_Error Root value on success or PEAR_Error on failure.
     * @access public
     * @see Math_Numerical_RootFinding_Common::validateEqFunction()
     * @see Math_Numerical_RootFinding_Common::getEqResult()
     * @see Math_Numerical_RootFinding_Common::isDivergentRow()
     * @see Math_Numerical_RootFinding_Newtonraphson::compute()
     */
    function compute($fxFunction, $dfx1Function, $dfx2Function, $xR)
    {
        // Validate f(x) equation function.
        $err = Math_Numerical_RootFinding_Common::validateEqFunction($fxFunction);
        if (PEAR::isError($err)) {
            return $err;
        }

        // Validate f'(x) equation function.
        $err = Math_Numerical_RootFinding_Common::validateEqFunction($dfx1Function);
        if (PEAR::isError($err)) {
            return $err;
        }

        // Validate f''(x) equation function.
        $err = Math_Numerical_RootFinding_Common::validateEqFunction($dfx2Function);
        if (PEAR::isError($err)) {
            return $err;
        }

        // Sets maximum iteration and tolerance from options.
        $maxIteration = $this->options['max_iteration'];
        $errTolerance = $this->options['err_tolerance'];

        // Sets variable for saving errors during iteration, for divergent
        // detection.
        $epsErrors = array();

        for ($i = 1; $i < $maxIteration; $i++) {
            // Calculate f(x[i]), where: x[i] = $xR.
            $fxR = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xR);

            // Calculate f'(x[i]), where: x[i] = $xR.
            $d1xR = Math_Numerical_RootFinding_Common::getEqResult($dfx1Function, $xR);

            // Calculate f''(x[i]), where: x[i] = $xR.
            $d2xR = Math_Numerical_RootFinding_Common::getEqResult($dfx2Function, $xR);

            // Avoid division by zero.
            if (pow($d1xR, 2) - ($fxR * $d2xR) == 0) {
                return PEAR::raiseError('Iteration skipped, division by zero');
            }

            // Newton-Raphson's formula.
            $xN = $xR - (($fxR * $d1xR) / (pow($d1xR, 2) - ($fxR * $d2xR)));

            // xR is the root.
            if ($xN == 0) {
                $this->root = $xR;
                break;
            }

            // Compute error.
            $this->epsError = abs(($xN - $xR) / $xN);
            $epsErrors[] = $this->epsError;

            // Detect for divergent rows.
            if ($this->isDivergentRows($epsErrors) &&
                $this->options['divergent_skip'])
            {
                return PEAR::raiseError('Iteration skipped, divergent rows detected');
                break;
            }

            // Check for error tolerance, if lower than or equal with
            // $errTolerance it is the root.
            if ($this->epsError <= $errTolerance) {
                $this->root = $xR;
                break;
            }

            // Switch x[i+1] -> x[i], where: x[i] = $xR and x[i+1] = $xN.
            $xR = $xN;
        }
        $this->iterationCount = $i;
        return $this->root;
    }

    // }}}
}

// }}}

/*
 * Local variables:
 * mode: php
 * tab-width: 4
 * c-basic-offset: 4
 * c-hanging-comment-ender-p: nil
 * End:
 */
?>

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